A former Federal Reserve adviser is joining with an activist group to argue for overhauls at the central bank that they say would distance it from Wall Street and make its activities more transparent and accountable to the public.

Dartmouth College economics professor Andrew Levin—special adviser to Ben Bernanke and Janet Yellen between 2010 and 2012 when they were Fed chairman and vice chairwoman—is pressing for the overhaul with Fed Up coalition activists.

Dartmouth College economics professor Andrew Levin, special adviser to then Fed Chairman Ben Bernanke between 2010 to 2012, is pressing for the overhaul with Fed Up coalition activists. Many of the proposed changes target the 12 regional Federal Reserve Banks, which are quasi-private and technically owned by commercial banks in their respective districts.

“A lot of people would be stunned to know” the extent to which the Federal Reserve is privately owned, Mr. Levin said. The Fed “should be a fully public institution just like every other central bank” in the developed world, he said in a conference call announcing the plan. He described his proposals as “sensible, pragmatic and nonpartisan.”

The former central bank staffer said he sees his ideas as designed to maintain the virtues the central bank already brings to the table. They aren’t targeted at changing how policy is conducted today. “What’s important here is that reform to the Federal Reserve can last for 100 years, not just the near term,” he said.

That said, what is being sought by Mr. Levin and the activists is significant and would require congressional action. Ady Barkan, who leads the Fed Up campaign, said the Fed’s current structure “is an embarrassment to America” and Fed leaders haven’t been “willing or able” to make changes.

A Federal Reserve spokesman declined to address the proposal.

Mr. Levin wants the 12 regional Fed banks to be brought fully into the government. He also wants the process of selecting new bank presidents—they are key regulators and contributors in setting interest-rate policy—opened up more fully to public input, as well as term limits for Fed officials.

Mr. Levin’s proposal was made in conjunction with the Center for Popular Democracy’s Fed Up coalition, a group that has been pressuring the central bank for more accountability for some time. The left-leaning group has been critical of the structure of the regional banks, and has been pressing the Fed to hold off on raising rates in a bid to make sure the recovery is enjoyed not just by the wealthy, in their view.

The proposal was revealed on a conference call that also included a representative from Bernie Sanders’s presidential campaign, although all campaigns were invited to participate.

Mr. Levin says the members of the regional Fed bank boards of directors, the majority of whom are selected by the private banks with the approval of the Washington-based governors, should be chosen differently. The professor says director slots now reserved for financial professionals regulated by the Fed should be eliminated, and that directors who oversee and advise the regional banks should be selected in a public process involving the Washington governors and local elected officials. These directors also should better represent the diversity of the U.S.

Mr. Levin also wants formal public input into the selection of new bank presidents, with candidates’ names known publicly and a process that allows for public comment in a way that doesn’t now exist. The professor also wants all Fed officials to serve for single seven-year terms, which would give them the needed distance from the political process while eliminating situations where some policy makers stay at the bank for decades. Alan Greenspan, for example, was Fed chairman from 1987 to 2006.

With multiple vacancies in recent years, the selection of regional bank presidents has become a hot-button issue. Currently, the leaders of the New York, Philadelphia, Dallas and Minneapolis Fed banks are helmed by men who formerly worked for or had close connections to investment bank Goldman Sachs.

Mr. Levin called for watchdog agency the Government Accountability Office to annually review and report on Fed operations, including the regional Fed banks. He also wants the regional Fed banks to be covered under the Freedom of Information Act. A regular annual review hopefully would insulate the effort from perceptions of political interference, Mr. Levin said.